Finite Group Databasebeta

C2×#21446121 #29681187

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21446121

Splittings

FittingC23×M16×C61 ⋊ C2
SylowC61 ⋊ C2×#1871

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC23×M16×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenterC23×M16D61
hypocenterC61C2×#1871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×M16

2050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 170742);